When the Wheatstone bridge shown in the figure is used to find the value of resistor $${R_x},$$ the galvanometer $$G$$ indicates zero current when $${R_1} = 50\,\Omega ,\,\,{R_2} = 65\,\Omega $$ and $$\,{R_3} = 100\,\Omega ,\,\,$$ If $${R_3}$$ is known with $$\, \pm 5\% \,$$ tolerance on its nominal value of $$100\,\Omega .$$ What is the range of $${R_x}$$ in Ohms?

An unbalanced $$DC$$ Wheatstone bridge is shown in the figure. At what value of $$p$$ will the magnitude of $${V_0}$$ be maximum?

A separately excited DC generator has an armature resistance of 0.1 $$\Omega$$ and negligible armature inductance. At rated field current and rated rotor speed, its open-circuit voltage is 200 V. When this generator is operated at half the rated speed, with half the rated field current, an un-charged 1000 μF capacitor is suddenly connected across the armature terminals. Assume that the speed remains unchanged during the transient. At what time (in microsecond) after the capacitor is connected will the voltage across it reach 25 V?

A DC motor has the following specifications: 10 Hp, 37.5 A, 230 V; flux/pole = 0.01 Wb, number of poles = 4, number of conductors = 666, number of parallel paths = 2. Armature resistance = 0.267 Ω. The armature reaction is negligible and rotational losses are 600 W. The motor operates from a 230 V DC supply. If the motor runs at 1000 rpm, the output torque produced (in Nm) is ________.